Physics Chapter 11

What is the difference in the force of gravity on a 1.0-kg mass at the bottom of the deepest ocean trench and that at the top of the highest mountain? Assume that g = 9.8 m/s2 at sea level. The radius of Earth at sea level is 6.37x106 m. The deepest trench is the Marianas Trench, south of Guam, which has a depth d = 1.103x104 m below sea level. The highest mountain is Everest in Nepal, which has a height of h = 8.847x103 m above sea level. The difference is

0.061 N

In a distant galaxy, a planet orbits its sun at a distance of 1.8x1012 m with a period of 108s. A second planet orbits the same sun at a distance of 9x1011 m. What is the period of the second planet?

0.35x108 s

The radius of the orbit of Earth around the Sun is 150x106 km. If the orbital periods for Earth and Venus are 365 and 225 days respectively, calculate the radius of orbit for Venus in astronomical units AU.

0.72 AU

A satellite whose mass is 1000 kg is in a circular orbit 1000 km above the surface of the earth. A space scientist wants to transfer the satellite to a circular orbit 1500 km above the surface. The amount of work that must be done to accomplish this is

1.71 GJ

Earth and Mars are 1.0 AU and 1.52 AU away from the Sun, respectively. Given that the period of Earth's orbit around the Sun is 1 yr, calculate the period of the orbit of Mars around the Sun. (1 AU = 150x106 km)

1.9 yr

An asteroid in orbit about the sun has a linear speed of 4 km/s when at a distance of closest approach d from the sun. What is its linear speed when it is at its greatest distance from the sun, a distance 2d?

2 km/s

If the mass of Earth is 6x1024 kg, the mass of the moon 7x1022 kg, the radius of the moon's orbit 4x108 m, and the value of the gravitational constant 6x10-11 Nm2/kg2, the force between Earth and the moon is approximately

2x1020 N

If the mass of Earth is 6x1024 kg, the mass of the moon 7x1022 kg, the radius of the moon's orbit 4x108 m, and the value of the gravitational constant 6x10-11 Nm2/kg2, the force between Earth and the moon is approximately

2x10^20 N

A certain object weighs 22.2 N on the surface of Earth. If the radius of the moon is 0.276 times the radius of Earth and the mass of the moon is 0.0123 times the mass of Earth, the object's weight on the surface of the moon is approximately

3.58 N

If the mass of Mars is 0.107 times that of Earth, and its radius is 0.530 that of Earth, estimate the gravitational acceleration g at the surface of Mars.

3.73 m/s2

One day a human being will land on Mars. Mars has a diameter of 6786 km and a mass of 6.42x1023 kg. If you weighed 834 N on Earth, how much would you weigh on Mars?

316 N

The acceleration due to gravity at the surface of Earth is g. The radius of Earth is RE. The distance from the center of Earth to a point where the acceleration due to gravity is g/9 is

3RE

The mean radius of Earth is about 6.436x106 m. A satellite in a circular orbit 3.20x106 m above the surface of Earth has an acceleration of approximately

4.36 m/s2

You are in a spaceship that has a mass of 13x104 kg and is 2.2x1012 m from a black hole near the center of the galaxy. The gravitational force exerted by the black hole on the spaceship is 46 N. The force on the ship when it has moved to one-third of its original distance from the black hole is

410 N

The mass of Earth is ME = 6.0x1024 kg, and the mass of the Sun is 2.0x1030 kg. They are a distance of 1.5x108 km apart. Calculate the acceleration of Earth due to the gravitational attraction of the Sun.

6.0x10-3 m/s2

What is the magnitude of the gravitational force acting on a 79.5-kg student due to a 60.0-kg student sitting 2.25 m away in the lecture hall?

6.29x10-8 N

Suppose that a satellite is in a circular orbit at a height of 2.00x106 m above Earth's surface. What is the speed of a satellite in this orbit?

6.90x103 m/s

With what velocity must a body be projected vertically upward from the earth's surface, in the absence of friction, to rise to a height equal to the earth's radius (6400 km)?

7.9x103 m/s

An asteroid is in orbit at 4 times the earth's distance from the Sun. What is its period of revolution?

8 years

Suppose a rocket is fired vertically upward from the surface of Earth with one-half of the escape speed. How far from the center of Earth will it reach before it begins to fall back? (Let g = 9.8 m/s2 and RE = 6370 km.)

8.5x103 km

An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 20 N. The radius of the planet is 4.0x106 m. What is the mass of Planet X?

9.6x1024 kg

Which of the following statements is one of Kepler's three laws of planetary motion?

A line joining any planet to the sun sweeps out equal areas in equal times.

When two masses are a distance R apart, each exerts a force of magnitude F on the other. When the distance between them is changed to 4R, the force is changed to

F/16

The Earth's orbit is closest to the Sun in January and farthest from the Sun in July. When is the Earth moving the fastest in orbit?

January

According to Newton's law of universal gravitation, if the distance between two bodies is tripled, the gravitational force between them is

None of these is correct.

Which statement best explains why the weight of an object of mass m is different on Mars than it is on the Earth?

The masses and radii of Mars and Earth are not the same.

A spring scale and a balance are used to weigh a body at the equator and later at a higher latitude, which has a different value for the acceleration due to gravity. Which of the following is a true statement concerning these weightings?

The readings of the spring scale are different. The readings of the balance are the same.

Taking the zero of potential energy to be at the infinite separation of two masses, consider the energy of a body in circular planetary motion. Which of the following statements is valid?

The total mechanical energy of the system is constant and negative.

Which one of the following statements concerning the two gravitational constants G, the universal gravitational constant, and g the magnitude of the acceleration due to gravity is true?

The value of G is the same everywhere in the universe, but the value of g is not.

Which of the following statements is true?

There is no point in the universe where gravity is precisely zero.

Kepler's second law of planetary motion states that the radius vector from the sun to a planet sweeps out equal areas in equal times. This relationship is a consequence of which of the following conservation principles?

angular momentum

Kepler's second law, "aline joining any planet to the Sun sweeps out equal areas in equal times" is based on which conservation principle?

conservation of angular momentum

A woman whose weight on Earth is 500 N is lifted to a height of two Earth radii above the surface of Earth. Her weight

decreases to one-ninth of the original amount.

Which of the following best describes the property of the period of orbital revolution for an Earth satellite?

greater when the orbital radius is larger

If the mass of a planet is doubled with no increase in its size, the escape speed for that planet is

increased by a factor of 1.4

As a satellite falls into a lower orbit, its speed _______.

increases

If the mass of a satellite is doubled while the radius of its orbit remains constant, the speed of the satellite is

not changed.

According to Kepler's first law, Halley's Comet circles the Sun in an elliptical path with the Sun at one focus of the ellipse. What is at the other focus of the ellipse?

nothing

Suppose a planet exists that has half the mass of Earth and half its radius. On the surface of that planet, the acceleration due to gravity is

twice that on Earth.

The acceleration due to gravity in the vicinity of Earth

varies inversely with the square of the distance from the center of Earth.